Journal of Business Finance & Accounting, 33(7) & (8), 961–978, September/October 2006, 0306-686X
doi: 10.1111/j.1468-5957.2006.00620.x
The Free Cash Flow Anomaly Revisited:
Finnish Evidence
Annukka Jokipii and Sami Vähämaa*
Abstract: This paper examines the performance of an investment strategy based on free cash
flows using financial statement data of Finnish companies during the period 1992-2002. The
analysis in this paper is motivated by the so-called free cash flow anomaly previously documented
e.g. in Hackel, Livnat and Rai (2000). Using annual financial statement information, we identify
large-capitalization companies with positive free cash flows, low free cash flow multiples, and low
financial leverage. Since a portfolio of these companies is found to consistently outperform the
market index, our results suggest that the free cash flow anomaly also exists in the Finnish stock
market.
Keywords: free cash flow, anomaly, stock returns, investment strategy, portfolio management
1. INTRODUCTION
Previous studies have identified many anomalies in cross-sections of average stock
returns (see Hawawini and Keim, 1995, for a survey). An extensive literature shows that
stock returns are related to variables such as firm size (Banz, 1981), financial leverage
(Bhandari, 1988), and earnings-to-price (Basu, 1983) and book-to-market-equity ratios
(Fama and French, 1992). Yet another, although somewhat less well-known, asset pricing
anomaly has been documented in Hackel, Livnat and Rai (1994 and 2000) and Hackel
and Livnat (1995). These studies demonstrate that an investment strategy based on
free cash flows can consistently outperform the market portfolio and several other
benchmarks. Moreover, the empirical findings provided in Hackel et al. (2000) indicate
that this free cash flow anomaly is not related to any of the previously documented
cross-sectional anomalies. The basic approach underlying Hackel et al. (1994 and
2000) and Hackel and Livnat (1995) is not, however, completely novel. Several authors
have previously shown that financial statements contain useful information beyond the
bottom line earnings figure for explaining future stock returns (see e.g., Lipe, 1986;
* The authors are both from the Department of Accounting and Finance, University of Vaasa, Finland.
They would like to thank an anonymous referee, Erkki K. Laitinen, Jiri Novak, and participants at the 2005
European Accounting Association Conference for valuable comments and suggestions. They also gratefully
acknowledge Joshua Livnat for his encouraging comments on a very first draft of this paper. (Paper received
March 2005, revised version accepted January 2006. Online publication August 2006)
Address for correspondence: Sami Vähämaa, Department of Accounting and Finance, University of Vaasa,
P.O. Box 700, FIN-65101 Vaasa, Finland.
e-mail: [email protected]
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JOKIPII AND VÄHÄMAA
Ou and Penman, 1989; and Ball, 1992). Furthermore, previous studies also demonstrate
that cash flows contain incremental information over earnings for explaining the crosssectional variation in stock returns (see e.g., Livnat and Zarowin, 1990; Ali, 1994; and
Kallunki et al., 1998).
This paper re-examines the free cash flow investment anomaly documented by
Hackel et al. (1994 and 2000) and Hackel and Livnat (1995) in a different market
setting. In this paper, annual financial statement data of Finnish companies are used
to identify large-capitalization companies with positive free cash flows, low free cash
flow multiples, and low financial leverage. The use of data from the small and thinly
traded Finnish stock market provides an expedient setting to examine whether the
empirical findings documented in Hackel et al. (1994 and 2000) and Hackel and
Livnat (1995) can be generalized. Furthermore, the accounting principles and financial
reporting standards used in Finland also differ from those applied in the US. Most
importantly, the Finnish accounting rules provide extensive opportunities for earnings
management (see e.g., Booth et al., 1996). As noted by Hackel et al. (1994), the free
cash flow investment strategy exploits the finding that instead of focusing on cash flows
of a company, investors tend to be earnings-oriented. Since the reported accounting
earnings in Finland are typically subject to earning management to a larger extent
than in most other countries (Booth et al., 1996; and Kallunki et al., 1998), the free
cash flow investment strategy may, a priori, be considered particularly attractive in
the Finnish stock market. On the other hand, due to the small number of publicly
traded companies, it may be difficult to reliably identify the consistent free cash flow
generators among the companies, and hence the free cash flow investment strategy
may not necessarily be successful in Finland.
Besides providing a backtest of the free cash flow anomaly with Finnish data, this
paper also extends Hackel et al. (1994 and 2000) and Hackel and Livnat (1995) in
several respects. First, we considerably simplify the portfolio selection rules applied
by Hackel et al. (1994 and 2000) and Hackel and Livnat (1995). In this study, four
simplistic portfolio selection criteria are used to identify large-capitalization companies
with positive free cash flows, low free cash flow multiples, and relatively low financial
leverage. Second, in order to ascertain whether the portfolio selection criteria may be
even further simplified, we also analyze the incremental contribution of individual
selection criteria on the performance of the free cash flow investment strategy.
Furthermore, because the relative performance of different investment strategies is
likely to be affected by market conditions, the performance of the free cash flow
strategy is examined separately in bull and bear markets. Fourth, as Fama and French
(1996) show that most of the previously documented cross-sectional anomalies may be
explained by a three-factor asset pricing model, we apply the Fama-French methodology
to examine the existence of the free cash flow anomaly. Finally, given that long-term
stock returns tend to be non-Gaussian, the conventional test statistics applied in Hackel
et al. (1994 and 2000) and Hackel and Livnat (1995) may lead to spurious inference.
Therefore, to avoid problems caused by non-Gaussian return distributions, we apply
recent bootstrapping techniques for statistical inference.
In brief, the empirical findings reported in this paper demonstrate that a portfolio of
large-capitalization companies with positive free cash flows, low free cash flow multiples,
and low financial leverage can consistently outperform the market portfolio. On
average, the 12-month buy-and-hold return for the free cash flow portfolio exceeds the
corresponding return for the market index by about 11.8%. Moreover, the cumulative
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return for the free cash flow portfolio during the 11-year sample period is 614%,
compared with the corresponding return for the market index of 144%. Even after
taking into account the systematic risk and other known risk factors, the companies
in the free cash flow portfolio still provide superior returns in comparison to the
market index. These results are surprisingly similar to the empirical findings reported
in Hackel et al. (1994 and 2000) and Hackel and Livnat (1995), and thereby confirm
that investors can earn abnormal returns with investment strategies based on free
cash flows. However, our results also demonstrate that most of the benefits of the
free cash flow strategy may be captured simply by investing in companies with positive
free cash flows. The performance of the strategy may then be fine-tuned by imposing
additional selection criteria. Finally, our empirical findings suggest that the free cash
flow investment strategy is particularly attractive in declining markets.
The remainder of this paper is organized as follows. Section 2 describes the data used
in the empirical analysis. The portfolio formation rules applied to select the companies
into the free cash flow portfolio are described in Section 3. The empirical findings and
robustness checks on the performance of the free cash flow investment strategy are
reported in Section 4. Finally, Section 5 provides concluding remarks.
2. DATA
The empirical analysis in this paper is performed using annual financial statement data
of all publicly traded Finnish companies during the period 1992-2002. The financial
statement data are obtained from the Thomson Financial Worldscope. In addition,
monthly stock market data of publicly traded Finnish companies covering the period
from June 1990 to May 2004 are used in the analysis. The HEX Portfolio Index is used
as a benchmark portfolio. The HEX Portfolio Index reflects the price developments
of stocks on the Main List of the Helsinki Stock Exchange. In this index, the weight
of a company is limited to 10% of the total market capitalization of the index. 1 The
stock market data for the years 1990-2000 are provided by the Helsinki Stock Exchange
(HSE) and the data for the latter part of the sample period are collected from the
Thomson Financial Datastream.
There are significant differences between the US and Finnish stock markets. Most
importantly, the Finnish stock market is a very small market and consists mainly of
relatively thinly traded stocks. The number of publicly traded companies listed on the
HSE was only 139 at the end of 2004. Therefore, in comparison to the US stock markets
of more than 12,000 firms, the Finnish stock market may be considered extremely small.
It is also worth noting that the HSE has been very technology-oriented since the late
1990s and has one decidedly dominant company, Nokia Oyj, which accounts for more
than 65% of the market capitalization of the HSE (see Junttila, 2003).
Besides the differences between the stock markets, the accounting principles and
financial reporting standards used in Finland during our sample period have also
differed from those applied in the US. 2 Moreover, there are important differences
in the objectives of financial reporting between Finland and the US. Whereas the
1 A single company, Nokia Oyj, accounts for a vast proportion of the market capitalization of the HEX
All-Share Index. Hence, instead of reflecting general market developments, the HEX All-Share Index tends
to follow Nokia.
2 Booth et al. (1996 and 1997), Kallunki et al. (1998) and Kallunki and Martikainen (2003) provide reviews
of Finnish accounting rules and income statements.
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objective of financial reporting in the US is to produce information that is useful for
making economic decisions, the Finnish accounting system endeavors to determine
distributable profits, which include not only dividends to shareholders but also interest
payments and taxes. Consequently, income statements have a major role in the Finnish
accounting system. Another distinct feature of financial reporting in Finland is that the
Finnish accounting rules provide extensive opportunities for earnings management,
and thus the reported accounting earnings tend to be subject to earnings management
to a larger extent than in most other countries (see e.g., Booth et al., 1996; and Kallunki
et al., 1998). Due to these aspects, the use of Finnish data provides an expedient setting
to examine whether the empirical findings documented in Hackel et al. (1994 and
2000) and Hackel and Livnat (1995) can be generalized.
3. PORTFOLIO SELECTION
Hackel et al. (1994 and 2000) and Hackel and Livnat (1995) show that a portfolio of
companies with consistent free cash flows, low financial leverage and low free cash flow
multiples substantially outperforms the market index and several other benchmarks.
They select the companies for the portfolio based on six to seven selection criteria. 3
Considering the limitations of the Finnish data, we are forced to simplify and modify
the selection criteria. In particular, in order to ensure that the number of companies
included in the free cash flow portfolio is sufficiently large, only the four key criteria
of Hackel et al. (1994 and 2000) and Hackel and Livnat (1995) are adopted in the
portfolio selection.
In this paper, the companies included in the free cash flow portfolio are identified
based on the following selection criteria:
(I) Free Cash Flow > € 0
(II) 5 <
(III)
Market Value
< 30
Free Cash Flow
Total Debt
< 10
Free Cash Flow
(IV) Market Value > € 70 million.
As a result of applying these four selection criteria, a portfolio of large-capitalization
companies with positive free cash flows, low free cash flow multiples, and low financial
leverage is constructed. Free cash flow is usually defined as all cash generated by
operations that can be distributed back to shareholders without affecting the current
level of growth. Hence, it can be thought of as the after-tax cash flow that would be
available to the company’s shareholders if the company had no debt. In this paper, we
follow the conventional definition of free cash flow, and estimate it as the net cash flow
from operating activities minus capital expenditures. The net cash flow from operating
activities, in turn, is defined as the sum of net income, all non-cash charges and credits
3 Most importantly, Hackel et al. (1994 and 2000) and Hackel and Livnat (1995) require that free cash flows
are positive and have increased in most recent years. Furthermore, they require that the companies have low
financial leverage and are priced at a reasonable level relative to the free cash flows they produce. Finally,
Hackel and Livnat (1995) and Hackel et al. (2000) select only companies with large market capitalization.
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(e.g., depreciation, amortization of intangibles, and deferred taxes), extraordinary
items, and net change in working capital. It should be noted that, in contrast to Hackel
et al. (1994 and 2000), we do not assume positive four-year average free cash flows, and
moreover, we do not assume any growth in free cash flows. However, our requirement
of positive free cash flow in only the most recent year is consistent with Hackel and
Livnat (1995).
The selection criterion of a low free cash flow multiple is applied to ensure that the
current stock price of the company is at a reasonable level relative to its free cash flows.
The free cash flow multiple is estimated by the ratio of market value of equity to the
free cash flow measure in the previous year. Hackel et al. (1994 and 2000) require that
the free cash flow multiple is between 5 and 20, whereas Hackel and Livnat (1995) use
an upper bound of 30. According to Hackel et al. (2000), the rationale for selecting
an upper bound of 20 is that the median multiple of S&P 500 companies is around
25. In Finland, the median free cash flow multiples are typically relatively low, or even
negative, because many companies have negative free cash flows. However, the median
free cash flow multiples of companies with positive free cash flows were around 60-70
during the sample period. Initially, we adopted directly the upper bound of 20 used in
Hackel et al. (1994 and 2000), but unfortunately the number of companies fulfilling
this selection criterion was insufficient. Therefore, consistent with Hackel and Livnat
(1995), an upper bound of 30 is applied in this paper. This upper bound for the free
cash flow multiple is considered appropriate to ensure that the companies are priced
at a reasonable level relative to the free cash flows they produce.
The criterion of a low debt multiple is applied to avoid selection of highly leveraged
companies with an unfavorable debt capacity for the free cash flow portfolio. The debt
multiple is estimated by the ratio of total debt to free cash flow. This criterion is adopted
directly from Hackel et al. (1994 and 2000) and Hackel and Livnat (1995). Finally, the
selection criterion of a market value of at least € 70 million is assumed to ensure that the
portfolio consists of relatively large companies that are sufficiently traded. The market
capitalization of a median company in the HSE during our sample period was about
€96 million. Initially, we experimented with a lower bound of € 100 million, which
would have been reasonably close to the median value, and also quite similar to
the criterion applied in Hackel et al. (2000). However, this lower bound for market
capitalization appeared to be too strict, as the number of companies fulfilling the
criterion at the beginning of the sample period was too small. Consequently, to ensure
that the free cash flow portfolio contains a reasonable number of companies, we were
forced to loosen the lower bound of the selection criterion to € 70 million.
The free cash flow portfolio is formed at the beginning of June each year. On June 1,
we calculate the free cash flows and estimate the free cash flow and debt multiples using
the annual financial statements for the previous year and the current market values of
the companies in order to identify the companies to be included in the free cash flow
portfolio. In Finland, companies typically release their financial statements in February
or March. 4 Therefore, we have at least two months to analyze the financial statement
4 The Finnish legislation requires publicly traded companies to publish their financial statements within
three months of the end of the fiscal year-end. About 98% of the companies listed on the HSE have a
December fiscal year-end, and thus these companies are required to release their financial statements before
the end of March. The financial statements of the remaining 2% of the companies are published during the
autumn, thus leaving us about 5 to 9 months to analyze these data before the portfolio formation date.
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data before the portfolio formation date. After applying the portfolio selection criteria,
we assume equal investments in each stock included in the portfolio, and a one-year
buy-and-hold investment strategy. 5
The number of companies fulfilling the selection criteria is relatively low in any year.
On average, the free cash flow portfolio includes only 12 companies, and the number
of companies ranged from 3 in 1992 to 16 in 2002. 6 However, the number of companies
included in the portfolio may be considered quite large relative to the number of all
publicly traded Finnish firms, as the portfolio includes, on average, about 10% of all
companies listed on the HSE. This should be contrasted with the average portfolio size
of 63 companies in Hackel et al. (2000), corresponding to less than 1% of all publicly
traded companies in the US. Indisputably, the large amount of listed companies in the
US enables Hackel et al. (2000) to apply much stricter criteria in portfolio selection, and
thus enables them to identify the consistent cash flow generators among the companies
more reliably. In any case, due to the low absolute number of companies included in
the portfolio, the free cash flow investment strategy is likely to be more relevant for
foreign investors who wish to hold some Finnish stocks than for Finnish investors who
wish to have a well-diversified portfolio.
Descriptive statistics of the selection criteria for the free cash flow portfolio are
reported in Table 1. The table reports median market values (in euro millions) and
the free cash flow and debt multiples for the companies selected in the free cash flow
portfolio and the corresponding medians for all publicly traded companies on the
Helsinki Stock Exchange. The median market values of the companies in the free cash
flow portfolio range from about €150 million in 1992 to about €970 million in 2000.
As can be seen from the table, the median company in the free cash flow portfolio is
always substantially larger than the market median. On average, the market value of
the median company in the free cash flow portfolio is about four times higher than
the market value of the median company on the HSE. Hence, the companies in the
constructed portfolio may definitely not be considered small-capitalization firms.
Table 1 also shows that the median free cash flow multiple of the companies in
the free cash flow portfolio is much higher than the median market multiple. Since
a considerable number of companies listed on the HSE had negative free cash flows
during the sample period, the reported median market free cash flow multiples are
extremely low. It may also be noted from Table 1 that the median free cash flow multiple
for the free cash flow portfolio appears to be relatively stable throughout the research
period. This is in sharp contrast to the highly volatile median free cash flow multiple
of the market portfolio. Like the free cash flow multiples, the median market debt
multiples reported in Table 1 are also very low because many companies on the HSE
had negative free cash flows during the sample period. Consequently, the median debt
multiple of the companies in the free cash flow portfolio clearly exceeds the median
market debt multiple.
Table 1 also reports the median free cash flow per share and the median dividend
per share for the companies in the free cash flow portfolio and the corresponding
5 For instance, on June 1, 2003, we use data from the 2002 financial statements to construct the free cash
flow portfolio, and then assume a 12-month buy-and-hold strategy from June 1, 2003 to May 31, 2004.
6 Although the number of companies included in the free cash flow portfolio is relatively low, the companies
are still well spread across different industries. Hence, the performance of the free cash flow investment
strategy should not be affected by industry specific risk factors.
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291.13
163.48
283.23
236.47
324.60
302.91
808.65
966.91
352.46
354.52
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
41.96
73.33
100.24
84.60
116.22
125.30
121.60
164.74
91.26
85.01
54.68
HSE
14.94
14.57
13.33
14.99
16.69
20.62
16.38
16.05
12.69
12.05
11.72
FCF
FCF
2.69
7.22
3.66
2.82
2.93
5.03
4.01
6.04
5.18
2.97
4.43
−1.18
5.01
6.69
2.67
12.30
8.74
−1.02
6.29
−3.63
−1.79
−0.89
−3.58
1.80
3.55
0.46
1.51
1.23
−0.06
0.46
−0.75
−0.06
−0.02
HSE
Debt Multiple
HSE
FCF Multiple
0.41
1.52
0.47
0.85
1.21
0.92
0.81
1.30
0.88
0.55
0.56
FCF
HSE
−0.27
0.11
0.27
0.10
0.16
0.08
−0.01
0.03
0.01
−0.01
0.01
FCFPS
0.21
0.29
0.09
0.32
0.50
0.48
0.62
0.59
0.53
0.34
0.73
FCF
DPS
0.04
0.10
0.17
0.25
0.25
0.34
0.29
0.25
0.22
0.22
0.22
HSE
13.06
15.27
10.97
9.17
10.60
12.13
13.90
13.06
10.20
14.28
12.69
FCF
HSE
−0.36
12.84
10.26
9.13
12.04
12.80
13.34
15.40
10.37
10.16
9.82
P/E
0.60
0.70
0.74
0.77
0.68
0.71
0.63
0.53
0.44
0.56
0.65
FCF
Beta
Notes:
The table reports medians of the portfolio selection criteria for the companies selected for the free cash flow portfolio (FCF) and the corresponding medians for all
publicly traded companies on the Helsinki Stock Exchange (HSE). The free cash flow multiple (FCF Multiple) is the ratio of market value of equity to free cash flow.
The debt multiple is the ratio of total debt to free cash flow. The table also reports the median free cash flow per share (FCFPS) and the median dividend per share
(DPS) for the companies in the free cash flow portfolio and the corresponding market medians. The market values are reported in euro millions and the per share
items in euros. Beta is estimated using the market model with monthly returns for the previous 36 months. The HEX Portfolio Index is used as a proxy for the market
return.
FCF
Year
Market Value
Table 1
Descriptive Statistics
THE FREE CASH FLOW ANOMALY REVISITED
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JOKIPII AND VÄHÄMAA
market medians. The median free cash flow per share of the companies in the free
cash flow portfolio is substantially higher than the median of the market portfolio.
Interestingly, the median free cash flow per share for all companies on the HSE was
negative in 1992, 1998 and 2001. The median dividend per share figures reported in
Table 1 show that the companies in the free cash flow portfolio paid about twice the
amount of dividends of the median market firm. 7 This is an important feature to note,
given that dividends were tax free income to investors in Finland during the sample
period. It can also be noted from Table 1 that the median P/E ratio of the free cash flow
portfolio is not substantially different from the market median, except in 1992. Finally,
Table 1 reports beta coefficients for the free cash flow portfolio. The reported betas
are estimated using the market model with monthly returns for the previous 36 months
and using the HEX Portfolio Index as a proxy for the market return. The betas have
ranged from 0.44 to 0.77 during the sample period, and hence the companies in the
free cash flow portfolio may be considered to have relatively low systematic risk. These
low betas are in contrast to the close to unity betas reported in Hackel et al. (1994 and
2000).
4. RESULTS
(i) The Empirical Setup
The buy-and-hold returns for the free cash flow portfolio are calculated as the equally
weighted average of returns for the individual stocks included in the portfolio. The
performance of the free cash flow investment strategy in comparison to the HEX
Portfolio Index is analyzed based on three different measures of abnormal returns
(AR 1 , AR 2 , and AR 3 ). The first measure, AR 1, is the conventional market adjusted
return, defined as:
AR1 = RFCF − R M ,
(1)
where R FCF denotes the return on the free cash flow portfolio and R M is the return on
the HEX Portfolio Index. The second measure of abnormal performance, AR 2, is the
market model adjusted return, calculated as:
AR2 = RFCF − α − βR M .
(2)
This measure of abnormal performance takes into account the systematic risk of the
companies included in the free cash flow portfolio. Finally, the third measure employed
7 The median dividend yield for the free cash flow portfolio also exceeds the market median, thereby
suggesting that the companies included in the portfolio may be classified as value stocks. Capaul et al. (1993)
and Fama and French (1998), among others, have documented that value stocks significantly outperform
growth stocks. Hence, the performance of the free cash flow strategy might simply be another manifestation
of the value stock premium. However, the P/E ratios reported in Table 1 provide no evidence that the
free cash flow portfolio would consist of value stocks, as the median P/E ratios for the portfolio are not
systematically lower than the market medians. In any case, we employ the Fama-French (1993) three-factor
model in the empirical analysis in order to ascertain that our results are not driven by the value premium. As
shown by Fama and French (1996), this three-factor model is able to explain the outperformance of value
stocks.
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in the empirical analysis, AR 3, is the Fama-French (1993) three-factor model adjusted
return, defined as:
AR3 = RFCF − R F − β (R M − R F ) − ϕSMB − ηHML,
(3)
where R f is the risk-free interest rate, SMB is the difference between the return on a
portfolio of small stocks and the return on a portfolio of large stocks, and HML is the
difference between the return on a portfolio of high book-to-market stocks and the
return on a portfolio of low book-to-market stocks. Fama and French (1996) show
that this three-factor asset pricing model can explain most cross-sectional anomalies
documented in the finance literature.
The parameters for the market model and for the Fama-French three-factor
model are estimated for each period using monthly stock returns for the previous
36-month period. In order to test whether the calculated abnormal returns are
statistically significant, we apply conventional t-tests and bootstrapping with 10,000
resamplings.
(ii) Performance of the Free Cash Flow Investment Strategy
Table 2 reports the 12-month buy-and-hold returns for the free cash flow portfolio
and the corresponding returns for the HEX Portfolio Index. As can be seen from the
table, the mean (median) annual return for the free cash flow portfolio is about 23.3%
(22.5%), while the mean (median) return for the HEX Portfolio Index is considerably
lower, being about 11.5% (12.0%). The reported minimum and maximum returns
also indicate that the free cash flow portfolio outperforms the market index. Table 2
moreover shows that the annual return for the free cash flow portfolio has been negative
in only three investment periods out of 11, whereas the return for the HEX Portfolio
Index has been negative in five periods, also including the three negative periods for
the free cash flow portfolio. Interestingly, it may also be noted from the market adjusted
returns that the HEX Portfolio Index outperformed the free cash flow strategy in four
consecutive years during the bull market at the end of the 1990s, and altogether in 5
out of 11 years. During these five years, the market index outperformed the free cash
flow portfolio on average by 8.3%. However, during the remaining six years the free
cash flow strategy outperformed the HEX Portfolio index by an impressive average of
28.6%. Consequently, the results as a whole advocate the usefulness of the free cash
flow investment strategy in the Finnish stock market.
The market adjusted returns reported in Table 2 confirm the superior performance
of the free cash flow portfolio. The mean annual market adjusted return is 11.8%.
A bootstrapping exercise suggests that this market adjusted return is statistically
significant. However, perhaps due to the extremely small number of observations, we
are unable to reject the null of zero mean with the conventional t-test. In order to take
into account the systematic risk of the companies in the free cash flow portfolio, we also
calculate market model adjusted returns. The mean market model adjusted return is
about 14.0%. Both the parametric and the non-parametric p-values indicate that the
free cash flow portfolio statistically significantly outperforms the market index even
after taking into account the systematic risk. Moreover, even after taking into account
the Fama-French (1993) size and book-to-market factors, the free cash flow portfolio
still appears to slightly outperform the HEX Portfolio Index, with a mean estimate of
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Table 2
Annual Returns
6/93–5/94
6/94–5/95
6/95–5/96
6/96–5/97
6/97–5/98
6/98–5/99
6/99–5/00
6/00–5/01
6/01–5/02
6/02–5/03
6/03–5/04
Mean
Parametric p-value
Non-parametric p-value
Median
Minimum
Maximum
No. of positive periods
No. of observations
FCF
HEX
AR 1
AR 2
AR 3
0.894
−0.154
0.446
0.380
0.361
−0.165
0.225
0.221
0.193
−0.184
0.351
0.233
(0.036)
(0.018)
0.225
−0.184
0.894
8
11
0.444
−0.078
0.120
0.418
0.424
−0.041
0.341
−0.270
−0.122
−0.207
0.239
0.115
(0.188)
(0.144)
0.120
−0.270
0.444
6
11
0.450
−0.076
0.325
−0.038
−0.063
−0.124
−0.116
0.491
0.314
0.023
0.112
0.118
(0.125)
(0.052)
0.023
−0.124
0.491
6
11
0.621
−0.104
0.351
0.050
0.062
−0.143
0.011
0.362
0.233
−0.085
0.180
0.140
(0.078)
(0.034)
0.062
−0.143
0.621
8
11
0.528
−0.058
0.274
−0.032
0.043
−0.121
−0.002
0.306
0.063
−0.049
0.021
0.088
(0.168)
(0.098)
0.021
−0.121
0.528
6
11
Notes:
The table reports 12-month buy-and-hold returns for the free cash flow portfolio (FCF) and for the
HEX Portfolio Index (HEX). The buy-and-hold returns are calculated as the equally weighted average of
returns for the individual stocks in the portfolio. AR 1 is the market adjusted return, calculated as R FCF −
R M , where R FCF denotes the return on the free cash flow portfolio and R M is the return on the HEX
Portfolio Index. AR 2 is the market model adjusted return, calculated as R FCF − α − βR M . AR 3 is the
Fama-French (1993) adjusted return, calculated as R FCF − R f − β(R M − R f ) − ϕSMB − ηHML, where
R f is the risk-free return, SMB is the difference between the return on a portfolio of small stocks and the
return on a portfolio of large stocks, and HML is the difference between the return on a portfolio of high
book-to-market stocks and the return on a portfolio of low book-to-market stocks. The parameters for the
market model and for the Fama-French three-factor model are estimated with monthly returns for the
previous 36 months. The parametric p-value for the null hypothesis of zero mean is based on a conventional
t-test. The non-parametric p-value is obtained via bootstrapping with 10,000 resamplings.
8.8%. This mean Fama-French adjusted return, however, is statistically significant only
at the 0.10 level.
Figure 1 plots the cumulative returns for the free cash flow portfolio and for the HEX
Portfolio Index from June 1993 to May 2004. The figure evidently demonstrates that the
free cash flow portfolio substantially outperformed the HEX Portfolio Index during the
sample period. The cumulative 11-year return for the free cash flow portfolio is about
614% while the corresponding return for the HEX Portfolio Index is 144%. It may also
be noted from Figure 1 that the HEX Portfolio Index clearly outperformed the free
cash flow portfolio during the exceptionally optimistic growth period from spring 1999
until spring 2000. However, after the global stock market correction started in March
2000, the free cash flow portfolio continued to provide positive returns, and hence
the gap between the cumulative returns plotted in Figure 1 widens significantly during
the latter part of the sample period. From June 2000 to May 2004, the returns for the
free cash flow portfolio are consistently higher than the returns for the market index.
C 2006 The Authors
C Blackwell Publishing Ltd. 2006
Journal compilation THE FREE CASH FLOW ANOMALY REVISITED
971
Figure 1
Cumulative Returns on the Free Cash Flow Portfolio (FCF) and the HEX Portfolio
Index (HEX)
As a result, the cumulative four-year return for the free cash flow portfolio of about
61% substantially exceeds the corresponding cumulative return for the HEX Portfolio
Index of −37%.
Table 3 reports summary statistics of the monthly returns for the free cash flow
portfolio and for the HEX Portfolio Index. The table shows that the mean (median)
monthly return for the free cash flow portfolio is about 1.7% (1.8%), while the mean
(median) monthly return for the HEX Portfolio Index is 0.9% (0.4%). As can be noted
from the table, the mean monthly return of the market index is statistically insignificant.
The outperformance of the free cash flow portfolio is also obvious in the reported
minimum and maximum returns. Moreover, Table 3 demonstrates that the return for
the free cash flow portfolio was positive for 83 months out of 132, while the return
for the HEX Portfolio Index was positive for only 71 months. However, it may also be
noted from Table 3 that the market index outperformed the free cash flow strategy
in 69 out of 132 months. During these months, the average underperformance of the
free cash flow portfolio is −2.8%, whereas the average outperformance of the portfolio
during the remaining 63 months is 4.7%. These figures indicate that the distribution
of monthly market adjusted returns is highly positively skewed, 8 and thus, the free cash
flow strategy appears to outperform the market index overall. Interestingly, Table 3
also shows that the standard deviation of the monthly returns for the free cash flow
portfolio is slightly lower than the standard deviation of the market index, thereby
suggesting that the free cash flow portfolio contradicts the fundamental mean-variance
theorem.
8 The skewness coefficient of the monthly market adjusted returns is 0.72.
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Table 3
Monthly Returns
Mean
Parametric p-value
Non-parametric p-value
Median
Minimum
Maximum
Standard deviation
No. of positive months
No. of observations
FCF
HEX
AR 1
AR 2
AR 3
0.017
(0.002)
(0.004)
0.018
−0.145
0.323
0.061
83
132
0.009
(0.127)
(0.124)
0.004
−0.213
0.221
0.067
71
132
0.008
(0.000)
(0.038)
−0.003
−0.135
0.231
0.007
63
132
0.002
(0.000)
(0.386)
−0.003
−0.086
0.262
0.001
59
132
0.006
(0.000)
(0.056)
0.001
−0.103
0.243
0.005
67
132
Notes:
The table reports monthly returns for the free cash flow portfolio (FCF) and for the HEX Portfolio
Index (HEX). AR 1 is the market adjusted return, calculated as R FCF − R M , where R FCF denotes the return
on the free cash flow portfolio and R M is the return on the HEX Portfolio Index. AR 2 is the market model
adjusted return, calculated as R FCF − α − βR M . AR 3 is the Fama-French (1993) adjusted return, calculated
as R FCF − R f − β(R M − R f ) − ϕSMB − ηHML, where R f is the risk-free return, SMB is the difference
between the return on a portfolio of small stocks and the return on a portfolio of large stocks, and HML is
the difference between the return on a portfolio of high book-to-market stocks and the return on a portfolio
of low book-to-market stocks. The parameters for the market model and for the Fama-French three-factor
model are estimated with monthly returns for the previous 36 months. The parametric p-value for the
null hypothesis of zero mean is based on a conventional t-test. The non-parametric p-value is obtained via
bootstrapping with 10,000 resamplings.
The mean market adjusted return suggests that the free cash flow portfolio
outperforms the market index by about 0.8% on a monthly basis. Both the parametric
and the non-parametric p-values indicate that the outperformance of the free cash flow
portfolio is statistically highly significant. The mean market model adjusted return
is also positive, being about 0.2%. A simple t-test suggests that this mean estimate
is statistically significant. However, the p-value based on the bootstrapping exercise
indicates that the market model adjusted return is not significant. Finally, the FamaFrench adjusted returns show that the free cash flow portfolio is more profitable than
the market index, as the mean is positive and statistically significant.
In brief, both the annual and monthly returns demonstrate that the free cash flow
investment strategy consistently outperforms the market index. The outperformance
of the free cash flow strategy is statistically significant even after taking into account
the systematic risk of the companies included in the portfolio and the Fama-French
(1993) size and book-to-market factors. These findings, together with the fact that the
free cash flow portfolio includes only large-capitalization companies with slightly above
median P/E ratios, suggest that the superior performance of the free cash flow strategy
is unlikely to be related to the cross-sectional anomalies previously documented in the
finance literature.
(iii) Robustness Checks
In order to examine the robustness of the findings reported in the previous section,
we analyze the incremental impact of individual selection criteria on the performance
of the free cash flow strategy. Furthermore, as an additional robustness check, we also
examine the performance of the strategy in different market conditions.
C 2006 The Authors
C Blackwell Publishing Ltd. 2006
Journal compilation THE FREE CASH FLOW ANOMALY REVISITED
973
The incremental impact of individual selection criteria is analyzed by constructing
three different portfolios. The first portfolio consists of all Finnish companies with
positive free cash flows, i.e. the portfolio satisfies selection criterion I. The second
portfolio includes companies with positive free cash flows and free cash flow multiples in
the range of 5-30, and thereby the companies in this portfolio fulfill selection criteria I
and II. Finally, the companies selected in the third portfolio are required to have
positive free cash flows and debt multiples of less than 10, and hence the portfolio
fulfills selection criteria I and III.
Panel A of Table 4 reports the monthly returns for portfolio 1. The results suggest
that a portfolio of companies with positive free cash flows slightly outperforms the HEX
Portfolio Index. The mean (median) monthly return for portfolio 1 is about 1.5%
(1.1%), while the corresponding mean (median) monthly return for the market index
is 0.9% (0.4%). The parametric p-values indicate that the outperformance of portfolio
1 is statistically highly significant. The non-parametric p-values, however, suggest that
the market model and the Fama-French adjusted returns are statistically insignificant.
The corresponding monthly returns for portfolios 2 and 3 are reported in Panels B
and C of Table 4. The mean market adjusted returns for these two portfolios are
positive, and thereby indicate that the portfolios outperform the HEX Portfolio Index.
The parametric p-values show that the market adjusted returns for portfolios 2 and
3 are statistically significant. However, the bootstrapped p-values indicate that the
market adjusted return for portfolio 3 is not significant. Furthermore, the bootstrapped
p-values also show that the market model and the Fama-French adjusted returns for
portfolios 2 and 3 are statistically insignificant.
In general, the results reported in Table 4 demonstrate that the outperformance of
the free cash flow investment strategy may to a large extent be attributed to the first
selection criterion, as a portfolio of companies with positive free cash flows appears to
outperform the market index by about 0.6% on a monthly basis. The corresponding
figure for the free cash flow portfolio that satisfies all four selection criteria is not much
higher, being 0.8%. Interestingly, the additional selection criteria imposed in portfolios
2 and 3 seem to have no noteworthy impact on the mean returns. In fact, the mean
monthly returns for portfolios 2 and 3 are even slightly lower than the corresponding
mean for portfolio 1. However, the additional selection criteria appear to decidedly
decrease the standard deviation of monthly returns.
A comparison of the results reported in Tables 3 and 4 suggests that it is nonetheless
justified also to impose the fourth selection criterion of a market value of at least
€70 million. The mean and median returns in Table 3 for the free cash flow portfolio
are higher, and furthermore, the adjusted returns are statistically more significant.
The bootstrapping exercise indicates that the market adjusted returns in Table 3 are
significant at the 0.05 level, while being significant only at the 0.10 level in Table 4 for
portfolios 1 and 2 and insignificant for portfolio 3. Moreover, the Fama-French adjusted
returns in Table 3 are also statistically significant contrary to the corresponding returns
in Table 4. In brief, our findings suggest that the first selection criterion already captures
most of the benefits of the free cash flow investment strategy. The performance of the
strategy may then be fine-tuned by imposing the additional three selection criteria.
Hence, the inclusion of all four selection criteria may be considered well-founded.
As noted in the previous section, Table 2 and Figure 1 indicate that the HEX Portfolio
Index outperformed the free cash flow portfolio during the exceptional bull market
at the end of the 1990s. However, it may also be noted from Table 2 and Figure 1 that
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JOKIPII AND VÄHÄMAA
Table 4
Incremental Contribution of Individual Selection Criteria on Monthly Returns
R
HEX
AR 1
AR 2
AR 3
Panel A: Portfolio 1
Mean
Parametric p-value
Non-parametric p-value
Median
Minimum
Maximum
Standard deviation
No. of positive months
No. of observations
0.015
(0.007)
(0.006)
0.011
−0.160
0.310
0.063
77
132
0.009
(0.127)
(0.124)
0.004
−0.213
0.221
0.067
71
132
0.006
(0.000)
(0.084)
0.005
−0.079
0.287
0.006
71
132
0.001
(0.000)
(0.662)
−0.002
−0.076
0.284
0.002
62
132
0.004
(0.000)
(0.156)
0.000
−0.097
0.252
0.005
67
132
Panel B: Portfolio 2
Mean
Parametric p-value
Non-parametric p-value
Median
Minimum
Maximum
Standard deviation
No. of positive months
No. of observations
0.013
(0.008)
(0.012)
0.010
−0.163
0.142
0.056
77
132
0.009
(0.127)
(0.124)
0.004
−0.213
0.221
0.067
71
132
0.004
(0.000)
(0.088)
0.003
−0.124
0.153
0.004
73
132
0.001
(0.000)
(0.694)
0.000
−0.110
0.095
0.002
67
132
0.000
(0.000)
(0.886)
0.001
−0.113
0.077
0.001
70
132
Panel C: Portfolio 3
Mean
Parametric p-value
Non-parametric p-value
Median
Minimum
Maximum
Standard deviation
No. of positive months
No. of observations
0.012
(0.024)
(0.036)
0.010
−0.169
0.168
0.058
78
132
0.009
(0.127)
(0.124)
0.004
−0.213
0.221
0.067
71
132
0.003
(0.000)
(0.378)
0.000
−0.108
0.100
0.003
66
132
0.000
(0.000)
(0.860)
0.001
−0.068
0.081
0.001
69
132
0.002
(0.000)
(0.516)
0.000
−0.072
0.087
0.002
65
132
Notes:
The table reports monthly returns for three different portfolios (R) and for the HEX Portfolio
Index (HEX). Portfolio 1 includes all companies with positive free cash flows (Criterion I), Portfolio 2
includes companies with positive free cash flows and low free cash flow multiples (Criteria I & II), and
Portfolio 3 includes companies with positive free cash flows and low debt multiples (Criteria I & III). AR 1
is the market adjusted return, calculated as R FCF − R M , where R FCF denotes the return on the free cash
flow portfolio and R M is the return on the HEX Portfolio Index. AR 2 is the market model adjusted return,
calculated as R FCF − α − βR M . AR 3 is the Fama-French (1993) adjusted return, calculated as R FCF − R f −
β(R M − R f ) − ϕSMB − ηHML, where R f is the risk-free return, SMB is the difference between the return on
a portfolio of small stocks and the return on a portfolio of large stocks, and HML is the difference between
the return on a portfolio of high book-to-market stocks and the return on a portfolio of low book-to-market
stocks. The parameters for the market model and for the Fama-French three-factor model are estimated
with monthly returns for the previous 36 months. The parametric p-value for the null hypothesis of zero
mean is based on a conventional t-test. The non-parametric p-value is obtained via bootstrapping with 10,000
resamplings.
the free cash flow strategy considerably outperformed the market index after the stock
market correction started in the spring of 2000. Hence, it is of interest to examine
the monthly performance of the free cash flow strategy separately in bull and bear
markets.
C 2006 The Authors
C Blackwell Publishing Ltd. 2006
Journal compilation 975
THE FREE CASH FLOW ANOMALY REVISITED
Table 5
Monthly Returns in Bull and Bear Markets
FCF
HEX
AR 1
AR 2
AR 3
Panel A: Bull Market, June 97 – May 00
Mean
0.011
Parametric p-value
(0.260)
Non-parametric p-value
(0.286)
Median
0.015
Minimum
−0.145
Maximum
0.117
Standard deviation
0.058
No. of positive months
23
No. of observations
36
0.020
(0.123)
(0.124)
0.018
−0.213
0.211
0.077
22
36
−0.009
(0.261)
(0.246)
−0.013
−0.130
0.091
0.048
11
36
−0.008
(0.201)
(0.230)
−0.010
−0.070
0.088
0.036
9
36
−0.004
(0.442)
(0.478)
−0.005
−0.081
0.065
0.033
14
36
Panel B: Bear Market, June 00 – May 03
Mean
0.006
Parametric p-value
(0.493)
Non-parametric p-value
(0.486)
Median
0.012
Minimum
−0.117
Maximum
0.106
Standard deviation
0.055
No. of positive months
20
No. of observations
36
−0.016
(0.154)
(0.150)
−0.024
−0.133
0.143
0.068
13
36
0.023
(0.003)
(0.002)
0.026
−0.048
0.176
0.045
23
36
0.008
(0.208)
(0.186)
0.007
−0.057
0.132
0.038
21
36
0.012
(0.035)
(0.042)
0.013
−0.055
0.110
0.034
24
36
Notes:
The table reports monthly returns for the free cash flow portfolio (FCF) and for the HEX Portfolio
Index (HEX) in bull and bear markets. AR 1 is the market adjusted return, calculated as R FCF − R M , where
R FCF denotes the return on the free cash flow portfolio and R M is the return on the HEX Portfolio Index.
AR 2 is the market model adjusted return, calculated as R FCF − α − βR M . AR 3 is the Fama-French (1993)
adjusted return, calculated as R FCF − R f − β(R M − R f ) − ϕSMB − ηHML, where R f is the risk-free return,
SMB is the difference between the return on a portfolio of small stocks and the return on a portfolio of
large stocks, and HML is the difference between the return on a portfolio of high book-to-market stocks
and the return on a portfolio of low book-to-market stocks. The parameters for the market model and for
the Fama-French three-factor model are estimated with monthly returns for the previous 36 months. The
parametric p-value for the null hypothesis of zero mean is based on a conventional t-test. The non-parametric
p-value is obtained via bootstrapping with 10,000 resamplings.
Table 5 reports the monthly returns for the free cash flow portfolio and the HEX
Portfolio Index in two distinct three-year subperiods, the bull market from June 1997 to
May 2000 and the bear market from June 2000 to May 2003. Panel A of Table 5 suggests
that the HEX Portfolio index slightly outperforms the free cash flow portfolio in bull
markets, as the mean (median) monthly return for the HEX Portfolio Index is about
2.0% (1.8%), while the mean (median) return for the free cash flow portfolio is 1.1%
(1.5%). However, both the parametric and the non-parametric p-values demonstrate
that the outperformance of the market index is not statistically significant.
Turning the focus to the bear markets, Panel B of Table 5 clearly demonstrates
that the free cash flow strategy provides superior returns in comparison to the HEX
Portfolio Index. The positive mean and median returns for the free cash flow portfolio
are in sharp contrast to the negative returns for the market index. The mean market
adjusted return in Panel B indicates that the free cash flow portfolio outperforms the
market index by about 2.3% on a monthly basis during bear markets. A simple t-test and
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JOKIPII AND VÄHÄMAA
Table 6
Monthly Returns During Market Downturns
Mean
Parametric p-value
Non-parametric p-value
Median
Minimum
Maximum
Standard deviation
No. of positive months
No. of observations
FCF
HEX
AR 1
AR 2
AR 3
−0.046
(0.000)
(0.000)
−0.033
−0.145
0.043
0.053
4
23
−0.086
(0.000)
(0.000)
−0.071
−0.213
−0.052
0.035
0
23
0.041
(0.000)
(0.000)
0.049
−0.053
0.176
0.046
19
23
−0.004
(0.708)
(0.662)
0.003
−0.086
0.098
0.045
13
23
0.000
(0.969)
(0.982)
0.002
−0.067
0.092
0.038
13
23
Notes:
The table reports monthly returns for the free cash flow portfolio (FCF) and for the HEX Portfolio
Index (HEX) during market downturns. Market downturn is defined as a month in which the HEX Portfolio
Index fell by more than 5 percent. AR 1 is the market adjusted return, calculated as R FCF − R M , where R FCF
denotes the return on the free cash flow portfolio and R M is the return on the HEX Portfolio Index. AR 2 is
the market model adjusted return, calculated as R FCF − α − βR M . AR 3 is the Fama-French (1993) adjusted
return, calculated as R FCF − R f − β(R M − R f ) − ϕSMB − ηHML, where R f is the risk-free return, SMB is
the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks,
and HML is the difference between the return on a portfolio of high book-to-market stocks and the return
on a portfolio of low book-to-market stocks. The parameters for the market model and for the Fama-French
three-factor model are estimated with monthly returns for the previous 36 months. The parametric p-value
for the null hypothesis of zero mean is based on a conventional t-test. The non-parametric p-value is
obtained via bootstrapping with 10,000 resamplings.
the bootstrapping exercise suggest that both the market adjusted and the Fama-French
adjusted returns in Panel B are statistically highly significant.
Finally, we analyze the performance of the free cash flow portfolio during market
downturns. ‘Market downturn’ is defined as a month in which the HEX Portfolio Index
fell by more than 5%. This occurred in 23 months during the sample period. The market
downturn analysis is motivated by Lakonishok et al. (1994), who claimed that unknown
risk factors are more strongly manifested during periods of market turbulence.
The results of the market downturn analysis are reported in Table 6. The table
shows that the return for the free cash flow portfolio was positive in four market
downturn months. The mean return for the HEX Portfolio Index during these market
downturns was −8.6%, compared with the corresponding mean return for the free cash
flow portfolio of −4.6%. The mean market adjusted return shows that the free cash
flow portfolio outperformed the market index by 4.1% during the downturn months.
This outperformance of the free cash flow strategy appears to be statistically highly
significant. However, the mean market model adjusted return is negative and statistically
insignificant and the mean Fama-French adjusted return is also indistinguishable from
zero. Together with the results reported in Table 5, these findings suggest that the
superior performance of the free cash flow strategy may not be attributed to unknown
risk factors that are typically manifested during periods of market turbulence.
5. CONCLUSIONS
This paper examines the free cash flow investment anomaly documented by Hackel
et al. (1994 and 2000) and Hackel and Livnat (1995) in a different market setting. In
C 2006 The Authors
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Journal compilation THE FREE CASH FLOW ANOMALY REVISITED
977
this paper, annual financial statement data of Finnish companies are used to identify
large-capitalization companies with positive free cash flows, low free cash flow multiples,
and low financial leverage. The use of Finnish data is considered to provide an expedient
setting to examine whether the empirical findings documented in Hackel et al. (1994
and 2000) and Hackel and Livnat (1995) can be generalized.
The empirical findings reported in this paper demonstrate that the free cash flow
anomaly also exists in the Finnish stock market. Our results show that a portfolio
of large-capitalization companies with positive free cash flows, low free cash flow
multiples, and low financial leverage consistently outperforms the market portfolio.
On average, the 12-month buy-and-hold return for the free cash flow portfolio exceeds
the corresponding return for the market index by about 11.8%. Moreover, the
cumulative 11-year return for the free cash flow portfolio is 614%, compared with the
corresponding return for the market index of 144%. Even after taking into account
the systematic risk and other known risk factors, the companies in the free cash flow
portfolio still provide superior returns in comparison to the market index. These results
are surprisingly similar to the empirical findings reported in Hackel et al. (1994 and
2000) and Hackel and Livnat (1995). Thus, consistent with the previous studies, the
results presented in this paper suggest that investors can earn abnormal returns with
investment strategies based on free cash flows.
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C 2006 The Authors
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